• 한국수학교육학회지시리즈B:순수및응용수학
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• 제17권1호
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• pp.65-80
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• 2010

In [17, 18], the fuzzy stability problems for the Cauchy additive functional equation and the Jensen additive functional equation in fuzzy Banach spaces have been investigated. In this paper, we prove the generalized Hyers-Ulam stability of the following quadratic functional equations in fuzzy Banach spaces: (0.1) f(x + y) + f(x - y) = 2f(x) + 2f(y), (0.2) f(ax + by) + f(ax - by) = $2a^2 f(x)\;+\;2b^2f(y)$ for nonzero real numbers a, b with $a\;{\neq}\;{\pm}1$.

• Journal of applied mathematics & informatics
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• 제5권2호
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• pp.507-516
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• 1998

In this study we are concerned with the problem of ap-proximating a locally unique solution of an equation on a Banach space. A semilocal convergence theorem is given for the Super-Halley method in Banach spaces. Earlier results have shown that the order of convergence is four for a certain class of operators [4] [5] [8] These results were not given in affine invariant form and made use of a real quadratic majorizing polynomial. Here we provide our re-sults in affine invariant form showing that the order of convergence is at least four. In cases that it is exactly four the rate of convergence is improved. We achieve these results by using a cubic majorizing polynomial. Some numerical examples are given to show that our error bounds are better than earlier ones.

• Journal of applied mathematics & informatics
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• 제26권1_2호
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• pp.407-416
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• 2008

In this paper, we study property ($B_2$) and property ($D_2$) and their implications.

• 충청수학회지
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• 제25권2호
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• pp.171-182
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• 2012

In this paper, for any fixed integer $n\;>\;m\;{\geq}\;1$, we investigate the generalized Hyers-Ulam stability of the following quadratic functional equation $f(nx+my)\;+\;f(nx-my)\;=\;mn[f(x+y)\;+\;f(x-y)]\;+\;2(n-m)[nf(x)\;-\;mf(y)]$ in ${p}$-Banach spaces, where $0\;<\;p\;{\leq}\;1$. And we prove the same stability of the above functional equation in 2-Banach spaces.

• Korean Journal of Mathematics
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• 제14권2호
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• pp.161-168
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• 2006

In this paper, we study property (${\beta}$) and B-convexity in reflexive Banach spaces. It is shown that k-uniform convexity implies B-convexity and property (${\beta}$). We also show that there is a Banach space with property (${\beta}$) which cannot be equivalently renormed to be B-convex.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제14권2호
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• pp.111-125
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• 2007

For an odd mapping, we study a generalized additive functional equation in Banach spaces and Banach modules over a $C^*-algebra$. And we obtain generalized solutions of a generalized additive functional equation and so generalize the Cauchy-Rassias stability.

• Journal of applied mathematics & informatics
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• 제41권3호
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• pp.469-485
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• 2023

In this paper, we investigate the Hyers-Ulam-Rassias stability for a Drygas functional equation g(u + v) + g(u - v) = 2g(u) + g(v) + g(-v) in the setting of quasi-Banach space using fixed point approach. Also, we give general results on hyperstability of a Drygas functional equation. The results obtain in this paper extend various previously known results in the setting of quasi-Banach space. Some examples are also illustrated.

• 대한수학회논문집
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• 제12권2호
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• pp.237-250
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• 1997

In this paper, we study the asymptotic behavior of orbits ${S(t)x}$ of an asymptotically nonexpansive semigroup $S = {S(t) : t \in G}$ for a right reversible semitopological semigroup G, defined on a weakly compact convex subset C of Banach spaces with Opial's condition for any $x \in C$.

• Journal of applied mathematics & informatics
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• 제33권1_2호
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• pp.45-60
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• 2015

This paper is concerned with the existence of mild solutions for partial neutral functional integrodifferential equations with infinite delay in Banach spaces. The results are obtained by using resolvent operators and Krasnoselski-Schaefer type fixed point theorem. An example is provided to illustrate the results.

• East Asian mathematical journal
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• 제19권1호
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• pp.103-111
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• 2003

In this paper, we will discuss some sufficient and necessary conditions for modified Ishikawa iterative sequence with mixed errors to converge to fixed points for asymptotically quasi-nonexpansive mappings in Banach spaces. The results presented in this paper extend, generalize and improve the corresponding results in Liu [4,5] and Ghosh-Debnath [2].